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A057940 Number of prime factors of 4^n + 1 (counted with multiplicity). 9
1, 1, 2, 1, 3, 2, 3, 1, 4, 2, 3, 3, 4, 2, 6, 2, 4, 4, 4, 2, 6, 3, 5, 3, 7, 3, 6, 3, 3, 4, 5, 2, 6, 4, 7, 5, 5, 4, 10, 3, 5, 5, 5, 4, 11, 2, 4, 3, 6, 6, 9, 2, 4, 6, 7, 5, 8, 3, 7, 6, 6, 4, 10, 2, 10, 7, 6, 4, 8, 4, 6, 7, 5, 2, 14, 4, 9, 5, 4, 4, 10, 4, 6, 8, 11, 4, 8, 3, 4, 8, 11, 4, 9, 5, 10, 4, 9, 8, 12, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Max Alekseyev, Table of n, a(n) for n = 1..553 (first 531 terms from Amiram Eldar)

S. S. Wagstaff, Jr., The Cunningham Project

FORMULA

a(n) = A057957(2n) - A057957(n). - T. D. Noe, Jun 19 2003

a(n) = Omega(4^n + 1) = A001222(A052539(n)). - Wesley Ivan Hurt, Jan 28 2014

a(n) = A054992(2*n). - Amiram Eldar, Feb 01 2020

MAPLE

with(numtheory); A057940:=n->bigomega(4^n + 1); seq(A057940(n), n=1..100); # Wesley Ivan Hurt, Jan 28 2014

MATHEMATICA

Table[PrimeOmega[4^n + 1], {n, 100}] (* Wesley Ivan Hurt, Jan 28 2014 *)

CROSSREFS

bigomega(b^n+1): A057934 (b=10), A057935 (b=9), A057936 (b=8), A057937 (b=7), A057938 (b=6), A057939 (b=5), this sequence (b=4), A057941 (b=3), A054992 (b=2).

Cf. A001222, A052539, A057957, A274903.

Sequence in context: A278573 A108663 A307314 * A097285 A057432 A302295

Adjacent sequences:  A057937 A057938 A057939 * A057941 A057942 A057943

KEYWORD

nonn

AUTHOR

Patrick De Geest, Oct 15 2000

STATUS

approved

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Last modified May 17 13:23 EDT 2022. Contains 353746 sequences. (Running on oeis4.)